Word Count : 347

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हमें यह जाँचना है कि दिया गया फलन $$ f(x,y)=xy+\frac{2}{x}+\frac{4}{y},\quad x>0,\;y>0 $$ क्या बिंदु $(x_0,y_0)=(1,1)$ पर Schwarz (Clairaut) प्रमेय की आवश्यकताओं को संतुष्ट करता है। --- ### Schwarz प्रमेय (Clairaut’s theorem) यदि $f(x,y)$ के दूसरे क्रम के मिश्रित आंशिक अवकलज $$ f_{xy} = \frac{\partial^2 f}{\partial y \partial x}, \quad f_{yx} = \frac{\partial^2 f}{\partial x \partial y} $$ सतत हों किसी पड़ोस में $(x_0,y_0)$ के, तो $$ f_{xy}(x_0,y_0) = f_{yx}(x_0,y_0) _____ ___ ________ _____ ___ ________ ____ ____ __________.
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